Alan is using the equation mg sin A = umg cos A to determine the coefficient of friction, u, between a flat rock and a metal ramp. Find u to the nearest hundredth, if the rock begins to slide at 19º.
mg*sin19 = u*mgcos19,
Divide both sides by mg:
sin19 = u*cos19,
u = sin19 / cos19 = 0.344.
To find the coefficient of friction, u, using the equation mg sin A = umg cos A, where A is the angle of inclination and m is the mass of the rock, we need to rearrange the equation and solve for u.
Given:
A = 19º (angle of inclination)
m = mass of the rock
Let's start with the given equation:
mg sin A = umg cos A
Divide both sides of the equation by mg:
sin A = u cos A
Divide both sides of the equation by cos A:
tan A = u
Now, we can solve for u by taking the tangent of the angle A:
u = tan A
Substitute the given angle A:
u = tan 19º
Using a calculator, find the tangent of 19º:
u = 0.3443...
Round the result to the nearest hundredth:
u ≈ 0.34
Therefore, the coefficient of friction, u, between the flat rock and the metal ramp is approximately 0.34 to the nearest hundredth.